Science, Technology, Engineering and Mathematics - Mathematics and Computational Thinking

In Mathematics 7, students will develop a comprehensive mathematical foundation that blends core concepts with real-world application. They will engage with numbers, algebra, geometry, and statistics in a way that enhances their problem-solving abilities and critical thinking. Through exploring patterns, relationships, and numerical operations, students will gain confidence in representing and manipulating different forms of data and expressions. 

Students will tackle practical challenges by applying mathematical models and reasoning, connecting theory with authentic scenarios such as financial literacy and spatial analysis. Algebraic thinking will empower them to express and analyze relationships between variables, fostering a deeper understanding of how changes affect outcomes.  

In geometry, students will explore the properties of shapes, angles, and measurements, applying their learning to solve meaningful problems and visualize transformations. 

Statistics and probability will encourage students to investigate data, draw insights, and make predictions based on evidence, refining their ability to interpret information critically. They will learn to choose the most effective methods for displaying and analyzing data, enhancing their decision-making skills.  

The Mathematics 7 experience will prepare students to see mathematics not just as isolated topics but as an interconnected discipline that equips them with tools to approach complex problems methodically and rationally. 

In Mathematics 8, students will deepen their understanding of number systems, algebra, geometry, measurement, and statistics, applying their skills to theoretical and real-world challenges. They will build on their number sense by exploring irrational numbers, applying exponent laws, and solving complex calculations. Through mathematical modeling, students will approach practical problems involving ratios, percentages, and rates, especially in contexts like measurement and finance. 

Students will advance their algebraic thinking by manipulating expressions, graphing and solving linear equations, and addressing inequalities. They will use linear relationships to interpret and solve problems, refining models and testing conjectures with digital tools for enhanced comprehension. 

Geometry will encourage students to apply metric units in solving problems involving perimeter, area, and volume of composite shapes and prisms. They will explore the Pythagorean theorem and solve problems related to circles and time, applying their understanding across multiple time zones. Three-dimensional coordinates and the principles of congruence and similarity will guide their analysis and problem-solving, supported by algorithmic testing. 

In statistics and probability, students will conduct data-driven investigations, understanding the impact of sampling and analyzing data distributions for meaningful comparisons. They will expand their knowledge of probability by studying combinations of events, using tables and diagrams, and running experiments and simulations to explore compound events. This will empower students to make data-informed decisions and strengthen their analytical and problem-solving skills.

The concepts course focuses on fluency. Students develop skills in choosing appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognize robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.

The regular course focuses on problem-solving. Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

The accelerated course focuses on reasoning. Students develop an increasingly sophisticated capacity for logical thought and actions, such as analyzing, proving, evaluating, explaining, inferring, justifying and generalizing. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.

Prerequisites: Completion of Mathematics 8 or department consent 

The concepts course focuses on fluency. Students develop skills in choosing appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognize robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.

The regular course focuses on problem-solving. Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

The accelerated course focuses on reasoning. Students develop an increasingly sophisticated capacity for logical thought and actions, such as analyzing, proving, evaluating, explaining, inferring, justifying and generalizing. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.

Prerequisites: Completion of Integrated Mathematics or department consent.

In Pre-Calculus Concepts, students will deepen their understanding of advanced algebraic concepts, focusing on the manipulation and analysis of a variety of functions.

They will explore quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions, applying these to solve complex real-world and abstract problems. Students will gain proficiency in graphing and interpreting these functions, confidently handling transformations, inverses, and compositions. They will also refine their skills in solving equations and inequalities, including linear systems and quadratic equations, and extend their learning to more advanced topics like rational exponents, radical functions, and sequences. Students will also explore the behavior and properties of these functions and apply algebraic techniques to solve problems across a range of contexts.

The course will emphasize how to use mathematical tools to represent, analyze, and solve problems involving data, probability, and real-world applications. In data analysis and statistics, students will engage in rigorous data interpretation, using statistical measures to analyze data sets and identify key trends, outliers, and patterns. They will deepen their understanding of probability, tackling problems involving compound events and analyzing distributions through simulations and experiments.

By the end of the course, students will have refined their problem-solving abilities, developed a strong foundation in mathematical reasoning, and applied algebraic and statistical concepts to interpret and model a wide variety of situations- skills that will serve them well in future academic and real-life scenarios.

Prerequisites: Completion of Algebra II or department consent.

This course serves as an introductory level course for students from diverse academic backgrounds. Whether it's opinion polls, drug trials or sports recaps, data and statistics are ever-present in our surroundings. Nevertheless, statistics can be manipulated and presented in such a way to prove any point that the presenter wants. Thus, as constant consumers of media, people must learn how to filter through bias and find meaning in the actual numbers to make data-driven decisions. The goal of this course is not only to turn students into critical analysts but also to give them the tools and resources to collect and display data with as little bias as possible. This course introduces sampling statistics and estimation, probability theory, statistical hypothesis testing, and simple linear regression. Students design a study to test that hypothesis; collect and analyze their own data; examine and run tests on that data; and finally, present the data to their peers to support their conclusions. Students also learn how to build probability models by observing data and design experiments to reduce variability.

Prerequisites: Algebra II, any 300 level English course (concurrently) and department consent

In Pre-Calculus, students will develop a strong grasp of essential mathematical concepts, including an in-depth understanding of functions, trigonometry, and analytic geometry. They will confidently analyze, transform, and apply a wide range of functions- polynomial, rational, exponential, logarithmic, trigonometric, and polar- solving complex problems and demonstrating their ability to model real-world scenarios.

Students will interpret and solve problems related to rates of change, periodic behavior, and optimization, utilizing appropriate mathematical frameworks. In doing so, they will refine their skills in algebraic manipulation and graphing, approaching problems from both analytical and technological perspectives to gain a deeper understanding of their solutions. 

As students explore analytic geometry, they will enhance their spatial reasoning, gaining insights into conic sections, vectors, and other geometric representations. They will deepen their understanding of the graphical behavior and applications of various functions, equipping them with tools for interpreting geometric shapes and solving spatial problems. Students will also be introduced to foundational calculus concepts, including limits and continuity, preparing them for future success in AP Calculus or other advanced mathematics courses.  

By the end of the course, students will have built a comprehensive mathematical toolbox, developed strong problem-solving abilities and critical thinking skills, and have an appreciation for how mathematical principles can be applied to understand and model the world around them.  

Prerequisites: Completion of Algebra II (B or above), MCT 301: Algebra III, or department consent 

In Calculus, students will develop a solid foundation in both differential and integral calculus, preparing them to confidently apply calculus concepts to analyze rates of change, optimize functions, and calculate areas. These skills will set the stage for more advanced mathematical studies and practical applications in various fields.  

Students will gain the ability to analyze and interpret rates of change in a variety of contexts, distinguishing between constant, average, and instantaneous rates. They will develop a deep understanding of limits, calculating them both graphically and analytically, including limits at infinity and limits approaching infinity. This will lay the groundwork for concepts like continuity and differentiability, which are critical for more advanced calculus topics. 

Students will learn the process of differentiation, applying it to find slopes of tangents and derive functions from first principles. They will master primary differentiation rules, including the power, chain, product, and quotient rules, to calculate derivatives of polynomial, exponential, logarithmic, and trigonometric functions. Students will develop an understanding of second derivatives and will be able to analyze increasing and decreasing functions, as well as locate stationary and inflection points. They will apply these skills to optimize functions, using calculus to solve practical problems involving rates of change. 

In integral calculus, students will learn to calculate both definite and indefinite integrals, understanding the Riemann integral and antidifferentiation. They will apply the Fundamental Theorem of Calculus and utilize techniques such as substitution to solve integrals. Students will become proficient in using integration to calculate areas under curves, between curves, and above curves. They will also apply integrals in real-world problems, including those involving displacement, velocity, acceleration, and distance traveled. 

By the end of the course, students will have developed a strong problem-solving mindset, refined their mathematical reasoning and analysis, and prepared themselves for more advanced studies in calculus and related fields. 

Prerequisites: Completion of MCT 303: Pre-Calculus or department consent

In AP Calculus AB, students will develop a comprehensive understanding of calculus concepts and will be able to analyze and interpret functions using limits, continuity, and derivatives.  

They will understand the concept of limits and will be able to calculate both one-sided and two-sided limits, including those involving infinity and asymptotic behavior. Students will determine the continuity of functions and will apply the Intermediate Value Theorem to assess the behavior of functions over intervals. 

Students will learn to differentiate a wide variety of functions, including polynomial, rational, trigonometric, exponential, and logarithmic functions. They will become proficient in applying key differentiation rules, such as the product, quotient, and chain rules, to find the derivatives of composite and complex functions. They will also analyze the behavior of functions through critical points, determining intervals of increase and decrease, concavity, and points of inflection. Additionally, students will apply the First and Second Derivative Tests to solve optimization problems, identifying maxima, minima, and other key features of functions. 

In integral calculus, students will compute both definite and indefinite integrals, and will understand the relationship between differentiation and integration, as outlined in the Fundamental Theorem of Calculus. They will apply various techniques of integration, including substitution and integration by parts, to solve problems involving area under curves, displacement, and other practical applications. Students will also be able to interpret the results of these calculations in real-world contexts. 

Students will apply mathematical modeling to real-world situations, using calculus concepts to solve complex problems and interpret the results effectively. They will learn to analyze differential equations and apply their understanding of calculus to problems involving rates of change in both theoretical and applied contexts, such as physics, economics, and biology. 

By the end of the course, students will have developed a deep understanding of calculus concepts and techniques, preparing them for further studies in mathematics, science, engineering, and related fields. They will be able to confidently apply calculus to solve real-world problems, demonstrating both theoretical understanding and practical application. 

Prerequisites: Completion of MCT 303: Pre-Calculus (B or above) or department consent

In AP Statistics, students will effectively collect, analyze, and interpret data, applying statistical concepts and techniques to real-world situations. They will understand the principles of designing experiments and surveys, including how to select appropriate sampling methods and identify potential sources of bias. They will also articulate the importance of randomness in sampling and understand its impact on inference. 

Students will describe and summarize data using various graphical representations, such as histograms, box plots, and scatterplots, as well as numerical measures, including mean, median, mode, variance, and standard deviation. They will analyze the distribution of data, identifying patterns, trends, and outliers, and will apply measures of central tendency and variability to interpret and compare data sets. 

In the context of probability, students will calculate probabilities using the rules of probability, including the addition and multiplication rules, and will understand conditional probability and independence. They will create and interpret probability distributions for discrete and continuous random variables, applying concepts such as expected value and standard deviation to evaluate risk and uncertainty. 

Students will conduct hypothesis tests and construct confidence intervals for proportions and means, employing appropriate tests and interpreting the results in context. They will understand significance levels, p-values, and Type I and Type II errors, and will be able to explain the implications of their findings in terms of statistical inference. 

Additionally, students will analyze relationships between two quantitative variables using correlation and regression, understanding how to calculate and interpret the correlation coefficient and the equation of the regression line. They will assess the fit of a model and make predictions based on their analyses. 

By the end of the course, students will have developed a strong foundation in statistical reasoning and data analysis, equipping them with the skills necessary to make informed decisions based on data. They will be well-prepared for further studies in statistics, mathematics, social sciences, and related fields, demonstrating proficiency in utilizing statistical methods to analyze and interpret complex data. 

Prerequisites: Completion of MCT 303: Pre-Calculus (B or above) or department consent

The only difference between the Pre-Calculus and AP Pre-Calculus courses is the requirement for AP Pre-Calculus students to take the AP Pre-Calculus exam in May.

Prerequisites: Completion of Algebra II (B or above) or department consent

In AP Calculus BC, students will analyze and interpret a wide range of functions using advanced concepts in limits, continuity, derivatives, and integrals. They will possess a deep understanding of limits, including evaluating indeterminate forms using L'Hôpital's Rule and analyzing the behavior of functions as they approach asymptotes. Students will apply the concept of continuity to analyze piecewise functions and effectively use the Intermediate Value Theorem. 

Students will differentiate complex functions, including those involving parametric and polar equations, and will be able to apply implicit differentiation to find the slopes of tangents. They will understand and apply all differentiation rules, including higher-order derivatives, and use them to solve problems involving motion, optimization, and related rates. Students will also analyze the behavior of functions through critical points, determining intervals of increase and decrease, concavity, and points of inflection, using the First and Second Derivative Tests. 

In integral calculus, students will compute both definite and indefinite integrals and apply the Fundamental Theorem of Calculus to relate differentiation and integration. They will utilize various techniques for integration, such as integration by parts, partial fractions, and trigonometric substitution. Students will also understand the concept of improper integrals and will be able to evaluate them when necessary. 

Additionally, students will explore sequences and series, learning about convergence and divergence tests, power series, and Taylor and Maclaurin series. They will be able to analyze and represent functions as series, using this understanding to approximate functions and solve complex problems. 

Students will use mathematical modeling to apply calculus concepts to real-world situations, interpreting results and communicating their findings effectively. They will also be prepared to analyze differential equations and apply calculus concepts to problems involving rates of change in both theoretical and applied contexts, spanning disciplines such as physics, economics, and engineering. 

By the end of the course, students will have developed a comprehensive understanding of both the theoretical foundations and practical applications of calculus. They will be well-prepared for further studies in mathematics, science, engineering, and related fields. Students will demonstrate proficiency in analyzing and solving complex mathematical problems, confidently applying advanced calculus concepts to real-world scenarios. 

Prerequisites: Completion of MCT 303: Pre-Calculus (B or above) or department consent

In Multivariable Calculus, students will analyze and interpret functions of multiple variables, developing a deep understanding of concepts such as limits, continuity, partial derivatives, and multiple integrals. They will understand how to extend the principles of single-variable calculus to higher dimensions, allowing them to evaluate limits and determine continuity for multivariable functions.  

Students will compute and interpret partial derivatives and utilize them in the context of optimization problems, employing techniques such as the method of Lagrange multipliers to find extrema subject to constraints. Students will visualize and describe surfaces in three-dimensional space, using level curves and contour plots to analyze the behavior of multivariable functions. They will also become proficient in calculating gradients, understanding their geometric interpretation as direction vectors of steepest ascent, and applying them to gradient fields and directional derivatives. 

In integration, students will evaluate double and triple integrals, applying various techniques such as Fubini's Theorem to compute volumes under surfaces and analyze mass and center of mass in applied contexts. They will also use transformations, including polar, cylindrical, and spherical coordinates, to simplify the evaluation of integrals.  

Students will gain expertise in vector calculus, understanding the concepts of vector fields, line integrals, and surface integrals. They will apply Green's Theorem, Stokes' Theorem, and the Divergence Theorem to relate integrals over regions in space to integrals over their boundaries, effectively using these theorems in the context of physical applications such as fluid flow and electromagnetic fields. 

By the end of the course, students will have developed a comprehensive understanding of multivariable calculus concepts and their applications, preparing them for advanced studies in mathematics, engineering, physics, and related fields. They will be equipped to analyze and solve complex problems involving multiple variables, utilizing both analytical and graphical techniques to interpret their results in a variety of contexts. 

Prerequisites: Completion of MCT  501: AP Calculus AB or MCT 551: AP Calculus BC with a grade of B or above, and department consent

Students will experience a thorough transition from high school mathematics to university-level coursework. Through a blend of theoretical instruction, practical exercises, and collaborative projects, students will refine their analytical thinking, logical reasoning, and mathematical communication skills. The course is designed to foster an appreciation for the beauty and utility of mathematics, encouraging students to engage meaningfully and enthusiastically with the subject. By the end of the course, students will have engaged in a comprehensive review and extension of foundational mathematical concepts, preparing them for the rigor and expectations of higher education. 

Students will explore a diverse range of topics, including complex numbers, vectors, matrices, integrating factors, mechanics, logic, proof methods, probability, statistical distributions, geometry, and hyperbolic trigonometry. They will gain insights into the arithmetic and geometric properties of complex numbers, master the algebra and applications of vectors and matrices, and learn techniques for solving differential equations using integrating factors. Mechanics will also be introduced, with an emphasis on the principles governing motion and forces. Furthermore, students will delve into mathematical logic and various proof methods, enhancing their capacity to construct and evaluate logical arguments. The curriculum will also cover fundamental concepts in probability and statistical distributions, providing a strong foundation for analyzing random phenomena. Advanced geometric topics will be revisited, and students will be introduced to the intriguing aspects of hyperbolic trigonometry. 

By the end of the course, students will possess a robust understanding of complex numbers, vectors, matrices, and calculus concepts. They will have honed their problem-solving abilities, developed strong logical reasoning skills, and gained confidence in applying mathematical principles to diverse and complex scenarios, equipping them with the necessary tools to excel in university-level mathematics. 

Prerequisites: Completion of MCT 601: Multivariable Calculus, and department consent

In Introduction to Computer Science, students will demonstrate a strong understanding of foundational concepts in computer science through a creative and project-based approach.  

Students will learn how to program using JavaScript, starting with basic syntax and transitioning to more complex programming constructs such as functions and control structures. They will create and host their own web pages using HTML and CSS, applying design principles to enhance user experience. They will also develop interactive web applications that utilize JavaScript for dynamic content and user engagement. Through practical projects, they will build a personal portfolio website showcasing their programming skills, web designs, and digital presentations. 

The course will also explore the historical and societal impact of computing, as well as the components of computer systems. Students will investigate various computer models, from historical examples to contemporary devices like smartphones and drones. Students will also examine the structure and impact of the Internet, studying network communication, data security, and digital citizenship.  

By the end of the course, students will have developed critical thinking skills by applying computational thinking practices to analyze and solve problems effectively. They will emerge with a solid foundation in programming, web development, and computational thinking. Students will be equipped to pursue further studies in computer science and apply their skills in creative and innovative ways, fostering a passion for technology and its potential to shape the world. 

Prerequisites: Department consent

In AP Computer Science Principles, students will understand and apply foundational concepts of computer science and computational thinking to solve real-world problems. They will learn how to analyze and interpret data, recognizing its significance in decision-making processes. Students will also demonstrate proficiency in using programming languages to create projects that showcase their understanding of algorithms, data structures, and programming constructs. 

Students will design and develop interactive applications and understand the principles of user-centered design, incorporating feedback to improve their work. They will apply computational thinking techniques, such as decomposition, pattern recognition, and abstraction, to break down complex problems into manageable components. 

In addition, students will explore the impact of computing on society, including ethical considerations, the importance of cybersecurity, and issues related to data privacy and digital citizenship. Moreover, they will understand how technology influences communication, collaboration, and creativity across various fields. 

Students will engage in collaborative programming projects, utilizing version control systems and project management tools to work effectively in teams. They will also reflect on their coding practices and the development process, identifying areas for improvement and growth. 

By the end of the course, students will have developed a solid foundation in computer science principles, equipping them with the skills necessary to pursue further studies in computer science, software development, and related fields. They will also be prepared to think critically about the role of computing in the world and to create innovative solutions to complex problems using technology. 

In AP Computer Science A, students will demonstrate a solid understanding of the principles of computer science through the use of the Java programming language. They will know how to write, test, and debug programs that solve complex problems, utilizing key concepts such as variables, data types, control structures, and object-oriented programming. 

Students will design and implement algorithms that utilize various data structures, including arrays, Array Lists, and classes. They will be proficient in using methods and recursion to enhance program functionality and efficiency. Students will analyze the performance of algorithms, understanding the concepts of time complexity and space complexity to evaluate efficiency and make informed decisions about the best approach to problem-solving. 

Students will effectively use abstraction to manage complexity in their programs, employing encapsulation and inheritance to create modular and reusable code. They will understand the significance of interfaces and polymorphism in developing flexible software solutions. 

In addition to programming skills, students will be equipped to think critically about ethical and societal issues related to computing, such as data privacy, cybersecurity, and the impact of technology on individuals and communities. They will discuss the role of computing in various fields and its potential to drive innovation and change. 

By the end of the course, students will have developed the skills and knowledge necessary to pursue advanced studies in computer science, software engineering, and related disciplines. They will also be prepared to take on challenges in programming and software development, equipped with a strong foundation in computational thinking and problem-solving skills. 

Prerequisites: Completion of MCT 121: Introduction to Computer Science, AP Computer Science Principles or department consent

In Topics in College-Level Computing, students will explore advanced concepts and applications in computer science beyond the AP curriculum. They will know how to engage with a variety of specialized topics, such as algorithms, data structures, software development methodologies, and the principles of artificial intelligence and machine learning. 

Students will analyze and implement complex algorithms, understanding their design and efficiency through rigorous theoretical analysis. They will work with advanced data structures, such as trees, graphs, and hash tables, applying these structures to solve intricate computational problems. 

Students will develop software using modern programming paradigms, including object-oriented, functional, and concurrent programming. They will understand best practices in software engineering, including version control, testing methodologies, and agile development processes, enabling them to create robust and maintainable code. 

The course will also introduce students to key topics in cybersecurity, data privacy, and ethical considerations in computing, allowing them to critically evaluate the societal impacts of technology. Students will engage in projects that require teamwork and collaboration, applying project management techniques to navigate the software development lifecycle effectively. 

Additionally, students will explore emerging trends in computing, such as cloud computing, big data analytics, the Internet of Things (IoT), and virtual reality (VR). They will gain insights into the creation of immersive environments and interactive experiences, understanding VR's potential applications across fields like entertainment, education, healthcare, and design. 

By the end of the course, students will have developed a comprehensive understanding of contemporary issues in computer science, preparing them for further studies in computer science or related fields, and equipping them with the skills to tackle real-world problems through innovative technological solutions. 

Prerequisites: Completion of MCT 522: AP Computer Science A, or department consent